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A Catalan surface all straight line generators of which intersect a fixed straight line, called an axis of the conoid. For example, a hyperbolic paraboloid is a conoid with two axes.

The position vector of a conoid is given by

where is a unit vector having the same direction as an axis of the conoid and is some function. For a right conoid , , and then its axis is a line of striction. A right conoid with is a helicoid.



[a1] M. Berger, B. Gostiaux, "Géométrie différentielle: variétés, courbes et surfaces" , Presses Univ. France (1987)
[a2] M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976)
How to Cite This Entry:
Conoid. I.Kh. Sabitov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098